Uniform attractors for a phase-field model with memory and quadratic nonlinearity

A phase-field system with memory which describes the evolution of both the temperature variation v and the phase variable chi is considered. This ther modynamically consistent model is based on a linear heat conduction law of Coleman-Gurtin type. Moreover, the internal energy linearly depends both on the present value of v and on its past history, while the dependence on ch i is represented through a function with quadratic nonlinearity. A Cauchy-N eumann initial and boundary value problem associated with the evolution sys tem is then formulated in a history space setting. This problem is shown to generate a non-autonomous dynamical system which possesses a uniform attra ctor. In the autonomous case, the attractor has finite Hausdorff and fracta l dimensions whenever the internal energy linearly depends on chi.